Against "interpretation" - Comments

[A. Neumaier]

an instrumentalist minimal interpretation. In such an interpretation, Hermitian operators represent macroscopic measurement apparatus, and their eigenvalues indicate the measurement outcomes (pointer positions) which can be observed, while inner products give the probabilities of obtaining particular measured values. With such a formulation, quantum mechanics remains stuck in the macroscopic world

... but still has the problem to say what probabilities mean. Observed are only frequencies, not probabilities.

The first stage of interpretation of the mathematical formalism establishes the connection to the empirical world as far as needed for everyday physics in the laboratory or at the particle collider.

This is presumably what @Dale calls objective interpretation.

ost physicists would also prefer to have some idea of what is behind those measurements and observational data, i.e. just how the microscopic world which produces such effects is really structured.

and this would be what he calls subjective interpretation.

 

[A. Neumaier]

Now, as to whether this section on interpretation is consistent with your view of interpretation depends a little on what is meant by “corresponds with reality”.

Yes. For me, experiment is an obvious part of everyday reality. If we deny it this status, nothing objective is left. Fo you, reality seems to be something metaphysical, unrelated to experience (of which experimental evidence is a part).

I would only agree that the objective interpretation is what makes a theory useful, and that is already part of the theory itself.

OK, so let me try to make your terminology precise, as I understand you.

1. A mathematical framework defines the concepts of a theory and develops their logical implications.
2. An objective interpretation relates the concepts of the theory unambiguously to experiment.
3. A subjective interpretation gives a metaphysical description underlying the objective interpretation.
4. A theory consists of its mathematical framework and its objective interpretation.
5. An interpretation consists of the objective interpretation of the theory and its subjective interpretation.
6. Thus the objective interpretation is the intersection of interpretation and theory.

Can we agree on that? Then I'll accept this terminology for the sake of our discussion.

 

[ftr]

But to his dying day thought it incomplete

It is incomplete in the sense that all couplings and mass are put in by hand and are not emergent from the theory

Mathematical formalisms such as the one presented in basic form in the previous chapter are in themselves rather abstract; they say nothing about concrete reality.

Although mass and couplings are part of concrete reality but see above.

 

[bhobba]

It is incomplete in the sense that all couplings and mass are put in by hand and are not emergent from the theory.

There are many reasons it's incomplete. Only time will tell us if they are resolvable or not.

Thanks
Bill

 

[Dale]

Fo you, reality seems to be something metaphysical

Yes, by definition “reality” is a concept which is defined by and studied in the philosophical discipline of ontology which is one of the major branches of metaphysics. It is not that I doubt that experiments are real, it is just that the whole concept of reality is a philosophical one that cannot be addressed by the scientific method.

OK, so let me try to make your terminology precise, as I understand you.

This is not my terminology. This is an effort to construct a compromise terminology for clarity here.

My terminology would not make use of subjective and objective. All of the objective parts would be theory and all of the subjective parts would be interpretation in my terminology with no overlap between theory and interpretation. I believe that is the standard usage of the word “theory” and although it less clear I also believe that is the standard usage of the word “interpretation”.

However, I think your previous post is good compromise terminology for the purposes of this discussion. It clarifies the concepts and allows the discussion to proceed. Let’s use it for now.

 

[Lord Jestocost]

There are many reasons it's incomplete.

Quantum mechanics might seem to be incomplete if one prefers to come back to the idea of an objective real world, i.e. the reality concept of classical physics.

 

[A. Neumaier]

It is not that I doubt that experiments are real, it is just that the whole concept of reality is a philosophical one that cannot be addressed by the scientific method.

I had always meant reality in the common sense, not in the philosophical sense; and I think wikipedia als has this usage - it makes sense to me that way. So please reread my previous posts, substituting everywhere experiment for reality, and measured for real.

However, I think your previous post is good compromise terminology for the purposes of this discussion. It clarifies the concepts and allows the discussion to proceed. Let’s use it for now.

Ok. So we agree that objective interpretation is a prerequisite for making quantum theory useful, since it is part of the scientific theory called quantum theory.

Then I think all relevant dispute in the quantum foundations is in the unsolved problem of giving a precise meaning to the objective interpretation of quantum mechanics in a way consistent with the mathematical framework (about which there is almost general agreement). It is here where the different interpretations differ. To check this, let me repeat my request from post #93; it was addressing precisely the objective interpretation part of quantum theory:

No, it is the operative definitions of how to relate mathematical concepts of the theory to measurable quantities that make a theory useful. This is not interpretation in the common nomenclature typically used here, regardless of what Born and Schrödinger thought about the issue.

So please spell out the operative definitions that relate the mathematical concepts of quantum theory to measurable quantities. You'll find that this is impossible to do independent of any of the interpretations of quantum mechanics that can be found in the literature. (Shut-up-and-calculate works only because it leaves the interpretation to the community without spelling out precisely what it consists of.)

(So according to our compromise terminology, and in agreement with the claim by @Demystifier in the insight article under discussion, we would have as many different quantum theories as there are interpretations of quantum mechanics. Because this is not the way spoken about quantum physics in practice - there is only one quantum theory - the shut-up-and-calculate part - and there are many interpretations, I believe that the compromise terminology is not reflecting actual practice, but for the moment we may ignore this to be able to proceed.)

 

[Dale]

So please spell out the operative definitions that relate the mathematical concepts of quantum theory to measurable quantities.

I don't know enough about quantum mechanics to do that. QM is not the only scientific theory and not the only place where interpretations arise.

However, even if I did know enough QM to do that I would not. Frankly, the obsession with interpretations is the reason why I stay out of the QM forum. I would like to know more about QM, but I have no interest whatsoever in becoming embroiled in the 10000 th pointless argument on the topic here. The constant deluge of such threads is a real turn-off for me, which is a pity because in my case it has diluted the educational mission of PF as a whole.

This insights article is not specifically about QM and frankly, I think that the current discussion about specific interpretations of QM in this thread is off-topic and I have suggested its removal. The QM forum's obsession with interpretations is not something that I want spreading to other parts of the forum.

I refuse to pick up any QM-related gauntlet. Let's keep the discussion general, about theories, interpretations, and the scientific method.

So according to our compromise terminology, and in agreement with the claim by @Demystifier in the insight article under discussion, we would have as many different quantum theories as there are interpretations of quantum mechanics

I think you are misusing the compromise terminology. The various interpretations of any given theory, when presented with a given experimental setup, would all predict the same quantitatively measurable outcomes, no?

 

[DarMM]

An interesting observation is that in math we generally do not worry about interpretations of probability - we either apply it as most books like Feller's classic do or we simply look at the consequences of the Kolmogorov axioms as books on rigorous probability theory do. People generally do not get caught up much in the interpretation issue - but in Quantum Theory we have all sorts of, how to put it, 'vigorous' discussions about it. That always has struck me as, well interesting.

Funnily enough I always thought QM was very similar to probability theory in this regard. Although most people just apply it, there is a pretty active community of debate on Foundations, e.g. Frequentist vs Kolmogorov vs De Finetti vs Jaynes. Famously summed up in I.J. Good's title "46656 Varieties of Bayesians" for the Third Chapter of his 1983 book "Good Thinking: The Foundations of Probability and Its Applications".

 

[A. Neumaier]

This insights article is not specifically about QM and frankly, I think that the current discussion about specific interpretations of QM in this thread is off-topic and I have suggested its removal.

Isn't this very strange? In view of the fact that the article begins with the very first sentence

I am against “interpretations” of Quantum Mechanics (QM)

and ends with the very last sentence

There are no interpretations of QM, there are only theories

the topic is clearly the non-interpretation of quantum mechanics, though the title is different, and the argument is made more abstractly.

The various interpretations of any given theory, when presented with a given experimental setup, would all predict the same quantitatively measurable outcomes, no?

For the case of quantum mechanics, that's the real question. I believe not, if taken literally. This is why even Nobel prize winners such as Weinberg and t'Hooft spend significant effort on the interpretation issue. Though they did it only after their retirement: While paid they researched more important issues and kept the issues on the back burner.

The various interpretations of quantum mechanics would predict it only by being quite liberal with the interpretation details, and assuming a lot about the culture of doing physical experiment (which is far more complex than what interpretations usually consider).

I answered the above though you want to keep the discussion off quantum mechanics. But then it becomes nearly empty. In most fields of science there is agreement on the interpretation, hence no way to discuss your question meaningfully. The only exceptions are quantum mechanics, statistical mechanics, and applied probability theory, which share some of the foundational problems.

But historically, the question whether light was wave or matter was another such topic, and the interpretations ultimately gave different predictions. These were checkable, which decided in favor of the wave nature, long before it was known what waved...

 

[A. Neumaier]

Funnily enough I always thought QM was very similar to probability theory in this regard. Although most people just apply it, there is a pretty active community of debate on Foundations, e.g. Frequentist vs Kolmogorov vs Di Finetti vs Jaynes. Famously summed up in I.J. Good's title "46656 Varieties of Bayesians" for the Third Chapter of his 1983 book "Good Thinking: The Foundations of Probability and Its Applications".

J. von Plato, Creating modern probability, Cambridge Univ. Press, Cambridge 1994.

discusses the history of the concept and interpretation of probability.L. Krüger, G. Gigerenzer and M.S. Morgan (eds.), The Probabilistic Revolution: Ideas in the Sciences, Vol. 2, MIT Press, Cambridge, MA, 1987.

discuss the history of probability in the various fields of application. L. Sklar, Physics and Chance, Cambridge Univ. Press, Cambridge 1993.

discusses the philosophical problems of the probability concept, with an emphasis on statistical mechanics.

 

[Dale]

the topic is clearly the non-interpretation of quantum mechanics,

Good point, but I personally will not participate in your QM interpretation fights. Those discussions have already completely deterred me from learning QM here.

For the case of quantum mechanics, that's the real question. I believe not, if taken literally.

the interpretations ultimately gave different predictions.

Then they are different theories, per the standard definition, and calling them merely different interpretations is somewhat of a misnomer.

In most fields of science there is agreement on the interpretation, hence no way to discuss your question meaningfully.

Whether there is agreement on the interpretation or not is irrelevant. The question is a question about science and the scientific method generally. QM doesn’t own a monopoly on these topics simply because the community argues more.

To do meaningful science you need a theory. The theory must include the objective interpretation. The subjective interpretation is scientifically unnecessary, and depending on the theory it may be controversial or non-controversial.

 

[bhobba]

Although most people just apply it, there is a pretty active community of debate on Foundations, e.g. Frequentist vs Kolmogorov vs Di Finetti vs Jaynes. Famously summed up in I.J. Good's title "46656 Varieties of Bayesians" for the Third Chapter of his 1983 book "Good Thinking: The Foundations of Probability and Its Applications".

You are probably correct (drats I used that word - probably). It's likely we get a rather different sample on this forum to what people using QM generally do. Certainly when I did my studies in probability and stats nobody worried about it, although as you advance you pick up that there is a debate about its foundations, just like there is debate about the foundations of math itself. I wasn't that attracted personally to the area, liking analysis better, but always enjoyed the lectures of the professor taking it - he was a funny guy so took more subjects in it than I had to. My view on foundations would likely be described as rigorously Kolmogorovian but intuitively frequentest.

Thanks
Bill

 

[DarMM]

My view on foundations would likely be described as rigorously Kolmogorovian but intuitively frequentest.

What! You degenerate!

Seriously though, yes I think the interpretation debate is much louder here (and on the net in general) than it is in day to day practice in physics. Now I think two things about this.

On the one hand I think that is because many in the interpretation "wars" don't realize that beyond a certain point there are currently no more no-go theorems and even though interpretation X might make more personal sense to you, that's as far as it goes. At a certain point you just have people saying position X is "obviously daft" not recognizing that every interpretation by necessity has something that classically is "obviously daft". Also often advocates of interpretations don't know the fully modern version of their interpretation and what they should be accepting with it. Just compare "Beginner's MWI" with it's basic idea of splitting universes, with the modern version that comes out from Wallace et al's work of uncountably infinite worlds, approximate splittings, human perspective being what possibly defines worlds, etc. People don't realize that a properly worked out version of their favorite interpretation has more "obviously daft" features than they think.

On the other hand I think people who don't engage with the interpretations aren't "pragmatists unconcerned with philosophical mumbo jumbo", there is something deeply strange about entanglement and measurement in quantum theory and when I've spoken to these people and shown them things like the Kochen-Specker theorem, Bell's theorem, PBR theorem, they then do become interested in interpretations, i.e. most physicists think there is nothing to this because they carry around a vague interpretation¹ that they don't think about much and really doesn't make much sense when analysed. Not because there isn't a problem and only a pedantic philosopher would think so.

¹The general impression I get is that they think the wave function is a real thing that undergoes collapse upon measurement, without really thinking how odd measurement as a fundamental is or what even is collapse. The almost pop science "It's in two places at once until observed"

 

[bhobba]

What! You degenerate!

You bet your sweet Bippy. I only study it to become an actuary so I can get the big bucks

On the other hand I think people who don't engage with the interpretations aren't "pragmatists unconcerned with philosophical mumbo jumbo", there is something deeply strange about entanglement and measurement in quantum theory and when I've spoken to these people and shown them things like the Kochen-Specker theorem, Bell's theorem, PBR theorem, they then do become interested in interpretations, i.e. most physicists think there is nothing to this because they carry around a vague interpretation that they don't think about much and really doesn't make much sense when analysed. Not because there isn't a problem and only a pedantic philosopher would think so.

Regardless of ones attitude to interpretation there is something quite deep going on with entanglement:
https://arxiv.org/abs/0911.0695

And indeed the program of describing a classical world purely with QM has made great strides but is still not quite there yet - maybe it never will be in which case Einstein may have the last laugh over his good friend Bohr. Interestingly, even though they were good friends, and admired each other greatly, as reported by Ohanian - 'When Bohr visited the institute in 1948, Einstein refused to meet with him. In a comical incident during this visit, Einstein sneaked into an office in which Bohr was having a discussion with Pais, and found himself suddenly face to face with Bohr – but he merely wanted to borrow some tobacco for his pipe from a tin sitting on a shelf.'. Maybe Einstein, who evidently was only a shadow of his former self in his later years, became sick and tired of debating with Bohr.

Thanks
Bill

 

[bhobba]

The general impression I get is that they think the wave function is a real thing that undergoes collapse upon measurement, without really thinking how odd measurement as a fundamental is or what even is collapse. The almost pop science "It's in two places at once until observed"

OMG - that's pretty close to my view when I started posting here about 10 years ago now. My views have changed a LOT, and even now are changing as I learn more - but not at the rate they did during my first few years of posting - I wince thinking about some of my early posts.

Thanks
Bill

 

[atyy]

People don't realize that a properly worked out version of their favorite interpretation has more "obviously daft" features than they think.

Copenhagen is agreed by many proponents to be obviously daft. Have you read Landau and Lifshitz's QM textbook? They say this in a polite way, perhaps too polite as not everyone gets their message.

 

[StoneTemplePython]

Funnily enough I always thought QM was very similar to probability theory in this regard. Although most people just apply it, there is a pretty active community of debate on Foundations, e.g. Frequentist vs Kolmogorov vs Di Finetti vs Jaynes. Famously summed up in I.J. Good's title "46656 Varieties of Bayesians" for the Third Chapter of his 1983 book "Good Thinking: The Foundations of Probability and Its Applications".

My view on foundations would likely be described as rigorously Kolmogorovian but intuitively frequentest.

I hope this doesn't need to be forked into another thread. I found the above to be alarming.

Kolmogorov was sympathetic to the frequentist interpretation advocated by Richard von Mises and in fact believed his axioms were Taylor Kolmogorov made for a frequentist concept of probability. Reference: pages 43-45 of Probability and Finance by Shafer and Vovk, which includes a translated letter from Kolmogorov regarding exactly this point. Also of interest, page x of the book's Preface

Vovk's work on the topics of the book evolved out of his work, first as an undergraduate and then as a doctoral student, with Andrei Kolmogorov, on Kolmogorov's finitary version of von Mises's approach to probability.

- - - - -
From what I can tell, the books referenced in the quote and in post 112 are about philosophy and general audience books/ writeups. They aren't math books. (I do happen to like Gigerenzer though.) People complain about general public books on QM all the time. I don't see why we shouldn't have similar sentiment here.

 

[DarMM]

I hope this doesn't need to be forked into another thread. I found the above to be alarming.

As did I, bhobba is one of those dangerous frequentists who use Kolmogorov's axioms for their own nefarious ends.

Kolmogorov was sympathetic to the frequentist interpretation advocated by Richard von Mises and in fact believed his axioms were Taylor Kolmogorov made for a frequentist concept of probability.

Kolmogorov did have a different view to von Mises though, the whole "propensities" view and is often listed separately to frequentism in books on interpretations of probability theory. Later in life he had the complexity interpretation, again different from von Mises's view. It's these views I listed above informally as "Kolmogorov". Some still argue¹ that the complexity view is a form of Frequentism, if you take that view replace "Frequentist vs Kolmogorov" with "von Mises vs Kolmogorov".

From what I can tell, the books referenced in the quote and in post 112 are about philosophy and general audience books/ writeups. They aren't math books. (I do happen to like Gigerenzer though.) People complain about general public books on QM all the time. I don't see why we shouldn't have similar sentiment here.

A similar sentiment regarding what though? There is a debate about foundations and interpretation in probability with various schools that disagree with each other. Jaynes for example is fairly scathing of Frequentism in his book "Probability Theory: The logic of Science". @A. Neumaier 's references simply discuss this issue. The complaints about general books on QM is more related to their sensationalist content, inaccuracies or often taking a specific view on things and providing that view as the explanation. @A. Neumaier 's books don't seem to be doing that. In fact I don't understand the connection at all. What sentiment should we have, ignore books discussing interpretational issues?

¹ Just like in QM there are debates about how to classify interpretations!

 

[Demystifier]

Then they are different theories, per the standard definition, and calling them merely different interpretations is somewhat of a misnomer.

My insight is precisely to point out that such standard definition is inadequate. It can be applied to other sciences too, but since this standard definition is rarely used in other sciences, this insight is in fact most relevant to QM.

 

[Dale]

My insight is precisely to point out that such standard definition is inadequate.

Yes, but I disagree with your reasoning. The definitions of theory and interpretation are not dependent on the status of other theories or interpretations.

The parts of T1 that are the mathematical framework and the mapping to experiment are theory, regardless of the presence or absence of T2. The remainder of T1 is part of the interpretation, again regardless of the presence or absence of T2. Nothing about the theory/interpretation status of T1 changes with the advent of T2 because the definitions of theory and interpretation do not reference the presence or absence of any other theory or interpretation in any way.

I see nothing inadequate in the standard definition of theory, it was simply misapplied in your example scenarios. You are complaining that the standard definitions “don’t make sense” but you never even write down those definitions and then you carelessly apply them in your scenarios.

It is a straw man argument in my opinion. Yes, you have shown that something doesn’t make sense, but it isn’t the standard definition of theory.

 

[Demystifier]

The parts of T1 that are the mathematical framework and the mapping to experiment are theory, regardless of the presence or absence of T2. The remainder of T1 is part of the interpretation, again regardless of the presence or absence of T2.

Fine, then let us apply this to Bohmian mechanics. It has the guiding equation that other versions of QM don't have. If this equation is part of the theory, then what is the interpretational part of Bohmian mechanics?

 

[Dale]

Fine, then let us apply this to Bohmian mechanics. It has the guiding equation that other versions of QM don't have. If this equation is part of the theory, then what is the interpretational part of Bohmian mechanics?

I can’t help you there. As I made pretty clear above I have little knowledge of and substantially less interest in QM interpretations.

It may be that the standard definitions are difficult to apply to one theory or interpretation. That could be a problem with the definitions, but it would be a different one from what you highlighted in your article. Alternatively, (more likely) it could be a problem with the theory/interpretation in question. Perhaps the authors of the theory/interpretation should clarify their work rather than rewrite definitions that work well elsewhere.

 

[Demystifier]

As I made pretty clear above I have little knowledge and substantially less interest in QM interpretations.

That's perfectly OK. I just hope that the destiny of the insight about the interpretations will be decided by someone who does have a knowledge and interest on this stuff.

 

[Dale]

That's perfectly OK. I just hope that the destiny of the insight about the interpretations will be decided by someone who does have a knowledge and interest on this stuff.

No need to worry about that. It will stay, I am just voicing my opinion about it as a participant, not as a moderator.

I don’t think that the standard definitions are in need of a major overhaul. If the specific case of BM causes problems then I think the “repair” belongs there.

 

[StoneTemplePython]

Kolmogorov did have a different view to von Mises though, the whole "propensities" view and is often listed separately to frequentism in books on interpretations of probability theory. Later in life he had the complexity interpretation, again different from von Mises's view. It's these views I listed above informally as "Kolmogorov". Some still argue¹ that the complexity view is a form of Frequentism, if you take that view replace "Frequentist vs Kolmogorov" with "von Mises vs Kolmogorov"...There is a debate about foundations and interpretation in probability with various schools that disagree with each other. Jaynes for example is fairly scathing of Frequentism in his book "Probability Theory: The logic of Science". @A. Neumaier 's references simply discuss this issue. The complaints about general books on QM is more related to their sensationalist content, inaccuracies

Set aside Jaynes for a moment, it's a very peculiar book: a polemic mixed with some deep math insights. (I've only read part of the book but he seems to use e.g. Feller as some kind of straw-man punching bag. It's unfortunate.) It also technically isn't one of the books I was referring to in my post.
- - - - -
I don't think there is debate about foundations in probability. Finite additivity isn't really used much (i.e. de Finetti lost). There is a standard set of axioms used and these come from Kolmogorov. There are debates on interpretations.

What I'm saying is that the further you get from Kolmogorov and actual math books, they tend to get sensationalist and inaccurate. Vovk and Shafer directly address on page 45 that a lot of mathematicians thought it was von Mises vs Kolmogorov for forms of frequentism. Kolmogorov didn't think that way, nor did others in USSR who worked closely with him. If you want to call them mildly different flavors of frequentism, that's ok by me. But it isn't sensationalist enough to sell wide audience books. And it certainly is not 'Kolmogorov vs Frequentism'.

n.b.
when you say Kolmogorov view of probability I assumed you meant the standard austere, axiomatic approach to mathematical probability, laid down by Kolmogorov. I've never heard someone use it to mean subsequent complexity work, especially in a line of discussion that talks "about Foundations". The former (axiomatic approach) quite literally is foundational. The latter is not. (As mentioned in italics in my prior post -- Kolmogorov also had a finitary version of von Mises' probability... the reality is Kolmogorov did a lot of different stuff in probability.)

I also will flag that I've read and like 2 or 3 books by Gigerenzer though they are tied in with psychology, misuse of probability, and public messaging not math per se.

 

[DarMM]

OMG - that's pretty close to my view when I started posting here about 10 years ago now. My views have changed a LOT, and even now are changing as I learn more - but not at the rate they did during my first few years of posting - I wince thinking about some of my early posts.

I would have been no different about ten years ago as well. Certainly in the last two years I've learned a lot on this topic, so you're not the only one here who thought stuff like that. The shameful thing is that I had quite a good knowledge of QFT from a mathematical perspective.

Copenhagen is agreed by many proponents to be obviously daft. Have you read Landau and Lifshitz's QM textbook? They say this in a polite way, perhaps too polite as not everyone gets their message.

I have, but quite a while ago. Would you have the page reference where they imply this? I'd love to have a look.

I can’t help you there. As I made pretty clear above I have little knowledge of and substantially less interest in QM interpretations.

Just to say, in my opinion if you ignore the interpretations and the issues they seek to tackle one has a weaker understanding of QM. I say this based on myself as per my reply to @bhobba above, as well as conversations with others. Bell's theorem, the PBR theorem, Hardy's theorem, all result from restricting interpretations and contain major insights into QM.

 

[DarMM]

Set aside Jaynes for a moment, it's a very peculiar book: a polemic mixed with some deep math insights. (I've only read part of the book but he seems to use e.g. Feller as some kind of straw-man punching bag. It's unfortunate.) It also technically isn't one of the books I was referring to in my post.
- - - - -
I don't think there is debate about foundations in probability. Finite additivity isn't really used much (i.e. de Finetti lost). There is a standard set of axioms used and these come from Kolmogorov. There are debates on interpretations.

This is just a difference in the use of the word "Foundations", which is sometimes used to include interpretations.

Also see the parts in bold.

"There is no debate in Foundations of probability if we ignore the guys who say otherwise and one of them lost anyway, in my view"

Seems very like the kind of thing I see in QM Foundations discussions.

"Ignore Wallace's work on the Many Worlds Interpretation it's a mix of mathematics and philosophical polemic" (I've heard this)
"Copenhagen has been shown to be completely wrong, i.e. Bohr lost" (also heard this)

I think if I asked a bunch of subjective Bayesians I'd get a very different view of who "won" and "lost".

Jaynes is regarded as a classic by many people I've spoken to, I'm not really sure why I should ignore him.

What I'm saying is that the further you get from Kolmogorov and actual math books, they tend to get sensationalist and inaccurate. Vovk and Shafer directly address on page 45 that a lot of mathematicians thought it was von Mises vs Kolmogorov for forms of frequentism. Kolmogorov didn't think that way, nor did others in USSR who worked closely with him. If you want to call them mildly different flavors of frequentism, that's ok by me. But it isn't sensationalist enough to sell wide audience books. And it certainly is not 'Kolmogorov vs Frequentism'.

I don't know why we're talking about best seller general audience books. (Although if somebody can turn an account on Kolmogorov's axioms into a international bestseller they deserve every cent they get!)

It also doesn't really matter if Kolmogorov himself viewed it as some major "battle", the point is that they are different views on probability theory and held by different groups today.

when you say Kolmogorov view of probability I assumed you meant the standard austere, axiomatic approach to mathematical probability, laid down by Kolmogorov. I've never heard someone use it to mean subsequent complexity work, especially in a line of discussion that talks "about Foundations".

"Foundations" here includes interpretations, so "Kolmogorov vs Jaynes" for example was meant in terms of their different views on probability. There are others like Popper, Carnap. Even if you don't like the word "Foundational" being applied it doesn't really change the basic point.

Also note that in some cases there is disagreement over which axioms should be the Foundations. Jaynes takes a very different view from Kolmogorov here, eschewing a measure theoretic foundation.

 

[Dale]

in my opinion if you ignore the interpretations and the issues they seek to tackle one has a weaker understanding of QM

And as a direct result of the constant bickering about interpretations I have a less than weak understanding of QM and a substantially weaker desire to fix it. I am skeptical that they are as beneficial as you say, but the constant arguments are certainly detrimental to me personally.

 

[DarMM]

I am skeptical that they are as beneficial as you say

Why? What do you base that on?

 

[Dale]

Why? What do you base that on?

My experience with philosophy in general and interpretations in relativity. And a lack of any personal benefit from reading the interpretations threads here, and the moderation issues they frequently generate.

 

[DarMM]

My experience with philosophy in general and interpretations in relativity.

Okay but note that many major textbooks in Quantum Mechanics (Landau and Lifshitz, Weinberg, Ballentine, Griffiths, Auletta et al and many more) have discussions on interpretations, in some cases a lengthy chapter is devoted to them. It's an important issue.

I can appreciate why you feel that way from the two sources you mentioned, but note very few introductory textbooks in Relativity have chapters about interpretations and foundational issues. The case is simply different in QM.

 

[DarMM]

And a lack of any personal benefit from reading the interpretations threads here, and the moderation issues they frequently generate.

Sorry I missed this the first time around.

I can appreciate this, but I would say that:
(a) One is unlikely to derive much benefit from interpretational and foundational discussions on most topics without a strong basis in that subject. Although I am aware of how such threads have developed over the forums past and yes heat/light tends to zero as thread length increases so I do appreciate how you feel on this.
(b) I wouldn't use how annoying threads are on a topic here to gauge it's role in a subject. Not to say I'd do differently if I were in your position, I'd probably be pretty tired off it as well.

Basically if you want to learn QM, just jettison the irritation from threads here and go read Auletta et al, I think you'll find the chapter on the measurement problem interesting, full of insight on QM and included in the textbook for a reason.

 

[atyy]

I have, but quite a while ago. Would you have the page reference where they imply this? I'd love to have a look.

I'll just quote the bits here (all from p3 of LL QM). I don't agree entirely with what they say, but they state the classical/quantum cut clearly, and already I think one would think it absurd. The part I don't entirely agree with is they stress the independence of measurement from the observer. However, I think this is not strictly wrong, since the drawing of the cut itself is presumably subjective, and hence the objectivity that one obtains is still a subjective objectivity.

"In this connection the "classical object" is usually called apparatus, and its interaction with the electron is spoken of as measurement. However, it must be emphasized that we are here not discussing a process of measurement in which the physicist-observer takes part. By measurement, in quantum mechanics, we understand any process of interaction between classical and quantum objects occurring apart from and independently of any observer."

The part where they politely point out that measurement is weird is:

"Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation."

Personally, I got the message. However, Bell (who helped Sykes translate) did think they were way too polite: https://m.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf

 

[atyy]

Set aside Jaynes for a moment, it's a very peculiar book: a polemic mixed with some deep math insights. (I've only read part of the book but he seems to use e.g. Feller as some kind of straw-man punching bag. It's unfortunate.) It also technically isn't one of the books I was referring to in my post.
- - - - -

Yes, am not a fan of Jaynes either for the polemic. At the very least, one can get non-uniqueness by considering the various Renyi entropies, instead of just using the Shannon one.

I don't think there is debate about foundations in probability. Finite additivity isn't really used much (i.e. de Finetti lost). There is a standard set of axioms used and these come from Kolmogorov. There are debates on interpretations.

I agree. Bayesians can use the Kolmogorov axioms, just interpreted differently. (And yes, interpretation is part of Foundations, but the Kolmogorov part is settled.)

I think interpretation is even settling, with de Finetti having won in principle, but in practice one uses whatever seems reasonable, or both as this cosmological constant paper did: https://arxiv.org/abs/astro-ph/9812133.

 

[bhobba]

And as a direct result of the constant bickering about interpretations I have a less than weak understanding of QM and a substantially weaker desire to fix it. I am skeptical that they are as beneficial as you say, but the constant arguments are certainly detrimental to me personally.

Outside this forum and on the internet in general I think that the issues of interpretation are very much a backwater. What I think hooks most people really into QM is its incredible beauty. For example chapter three of Ballentine was a revelation to me - Schrodinger's equation etc really comes from symmetry. Then you see how the path integral approach explains the Principle Of Least Action and you realize that everything is really quantum. The appreciation of symmetry's power in physics reaches it full flowering in QM and QFT. To me that has been the most startling revelation of modern physics and has nothing to do with issues of interpretation. I personally find QM even more beautiful than GR which is generally considered the beautiful theory of physics. But GR, even though I was once heavily into it, seems to have lost its sparkle when I returned to it after becoming a mentor and wanting to widen the scope of my involvement with PF beyond QM. I found with Lovelock's Theorem, which I knew before, but hadn't really thought about its power, has killed a lot of the magic of GR for me. The theorem itself is magical, but it doesn't leave much mystery for me. Now combining GR and QM - that's another matter - it intrigues me greatly. I want to understand better than I do the following paper:
https://arxiv.org/abs/1209.3511

I am now pretty hooked on the EFT approach to quantum gravity and others seem as well eg:
https://blogs.umass.edu/donoghue/research/quantum-gravity-and-effective-field-theory/

Trouble is I am now 63 and things that came easy in my youth now take longer - but it is still possible to learn - it just takes longer.

Thanks
Bill

 

[DarMM]

The appreciation of symmetry's power in physics reaches it full flowering in QM and QFT. To me that has been the most startling revelation of modern physics and has nothing to do with issues of interpretation. I personally find QM even more beautiful than GR which is generally considered the beautiful theory of physics. But GR, even though I was once heavily into it, seems to have lost its sparkle when I returned to it after becoming a mentor and wanting to widen the scope of my involvement with PF beyond QM. I found with Lovelock's Theorem, which I knew before, but hadn't really thought about its power, has killed a lot of the magic of GR for me

Didn't know Lovelock's theorem, very interesting!

Symmetries in QM are incredible, especially as the link between the conserved quantities and transformations is so much closer than it is in classical mechanics and as you said it doesn't have anything to do with interpretations.

For @Dale , as @bhobba said interpretations are much bigger here and on the net than they are "on the ground" in physics, so I wouldn't let the issue put one off. On a personal level I in fact I only recall two discussions about it over the last eleven years.

Note that many physicists don't know much about the Fiber Bundle view of Yang Mills. It's a bit like that, not crucial, certainly not common, but worth knowing in my opinion as it gives one a deeper appreciation of certain aspects of the theory.

 

[A. Neumaier]

Basically if you want to learn QM, just jettison the irritation from threads here and go read Auletta et al, I think you'll find the chapter on the measurement problem interesting, full of insight on QM and included in the textbook for a reason.

Apart from the textbook ''Quantum Mechanics'' by Auletta, Fortunato, and Parisi 2009, there is also a book ''Foundations and Interpretation of Quantum Mechanics'' by Auletta 2001 , with many historical details, explaining among others why interpretation is important in quantum mechanics, and why it is controversial.

 

[A. Neumaier]

All of the objective parts would be theory and all of the subjective parts would be interpretation in my terminology with no overlap between theory and interpretation.

How would you differentiate between objective and subjective? How is measurement, or an electron, or a particle position, or an ideal gas, or a laser, or a Geiger counter, etc. - defined objectively? Truly objective is only the mathematical framework!

 

[Dale]

How would you differentiate between objective and subjective?

We already discussed that, didn’t we? Anything necessary to predict the outcome of an experiment is objective.

Truly objective is only the mathematical framework!

No, you cannot predict the outcome of an experiment with only the mathematical framework.

 

[bhobba]

How would you differentiate between objective and subjective? How is measurement, or an electron, or a particle position, or an ideal gas, or - defined objectively?

That is an issue Gell-Mann and others are grappling with in trying to complete the decoherent histories program. Progress has been made, but problems remain.

Thanks
Bill

 

[DarMM]

That is an issue Gell-Mann and others are grappling with in trying to complete the decoherent histories program. Progress has been made, but problems remain.

Thanks
Bill

Is there a good guide to open problems anywhere? I just finished Griffith's book "Consistent Histories" today and I'm eager to know more.

 

[bhobba]

Is there a good guide to open problems anywhere? I just finished Griffith's book "Consistent Histories" today and I'm eager to know more.

I think you have to look at some of the papers eg:
https://arxiv.org/abs/1312.7454

Thanks
Bill

 

[A. Neumaier]

We already discussed that, didn’t we? Anything necessary to predict the outcome of an experiment is objective.

This begs the issue. What is is that is necessary to predict the outcome? How do you differentiate between the necessary and the unnecessary?

An experiment tells, for example that when you point an unknown very weak source of light to a photodetector, it will produce every now and then an outcome - a small photocurrent, measured in the traditional way. Nothing predicts when this will happen. Predicted is only the average number of events in dependence on the assumed properties of the incident light, in the limit of an infinite long time - assuming the source is stationary. Nowhere photons, though the experimenters talk about these in a vague, subjective way that guides them to a sensible correspondence between their assumptions and the theory. All this is murky waters from the point of view of the subjective/objective distinction.

 

[A. Neumaier]

No, you cannot predict the outcome of an experiment with only the mathematical framework.

Only in as far as the outcome involves subjective elements.

In his famous textbook [H.B. Callen. Thermodynamics and an introduction to thermostatistics, 2nd. ed., Wiley, New York, 1985.] (no quantum theory!), Callen writes on p.15:

Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory.

At first sight, this sounds like a circular definition (and indeed Callen classifies it as such). But a closer look shows there is no circularity since the formal meaning of ''consistently described by thermodynamic theory'' is already known. The operational definition simply moves this formal meaning from the domain of theory to the domain of reality by defining when a real system deserves the designation ''is in an equilibrium state''. In particular, this definition allows one to determine experimentally whether or not a system is in equilibrium.

Nothing else is needed to relate a mathematical framework objectively to experiment.

What is ''consistent'' in the eye of a theorist or experimenter is already subjective.

 

[Dale]

Nothing else is needed to relate a mathematical framework objectively to experiment.

Ok, I have a mathematical framework: $a=bc$. Using nothing more than that framework, what is the objective relationship to experiment?

 

[A. Neumaier]

Ok, I have a mathematical framework: $a=bc$. Using nothing more than that framework, what is the objective relationship to experiment?

This is not the framework of a physical theory. It is just a mathematical formula.

According to Callen, if it were the mathematical framework of a physical theory it would predict that whenever you have something behaving like a and b, the product behaves like c. That's fully objective, and as you can see, needs a subjective interpretation of what a,b,c are in terms of reality (i.e, experiment).

A mathematical framework of a successful physical theory has concepts named (the objective interpretation part) after analogous concepts from experimental physics, in such a way that a subjective interpretation of the resulting system allows the theory to be successfully applied.M. Jammer, Philosophy of Quantum Mechanics, Wiley, New York 1974.

gives on p.5 five axioms for quantum mechanics (essentially as today), and comments:

p.5: ''The primitive (undefined) notions are system, observable (or "physical quantity" in the terminology of von Neumann), and state.''

p.7: ''In addition to the notions of system, observable, and state, the notions of probability and measurement have been used without interpretations.''

That's the crux of the matter. Since the properties of probability and measurement are not sufficiently specified in the framework, they remain conceptually ill-defined. Therefore one cannot tell objectively whether something on the level of experiments is consistent with the framework. One needs subjective interpretation.

And indeed, Jammer says directly after the above statement:

Although von Neumann used the concept of probability, in this context, in the sense of the frequency interpretation, other interpretations of quantum mechanical probability have been proposed from time to time. In fact, all major schools in the philosophy of probability, the subjectivists, the a priori objectivists, the empiricists or frequency theorists, the proponents of the inductive logic interpretation and those of the propensity interpretation, laid their claim on this notion. The different interpretations of probability in quantum mechanics may even be taken as a kind of criterion for the classification of the various interpretations of quantum mechanics. Since the adoption of such a systematic criterion would make it most difficult to present the development of the interpretations in their historical setting it will not be used as a guideline for our text.

Similar considerations apply a fortiori to the notion of measurement in quantum mechanics. This notion, however it is interpreted, must somehow combine the primitive concepts of system, observable, and state and also, through Axiom III , the concept of probability. Thus measurement, the scientist's ultimate appeal to nature, becomes in quantum mechanics the most problematic and controversial notion because of its key position.

 

[Dale]

This is not the framework of a physical theory.

It is a perfectly valid mathematical framework, one of the most commonly used ones in science.

It is your claim (as I understand it) that objective science can be done with only a mathematical framework. I think that is obviously false, as shown here.

 

[A. Neumaier]

It is a perfectly valid mathematical framework, one of the most commonly used ones in science.

It is your claim (as I understand it) that objective science can be done with only a mathematical framework. I think that is obviously false, as shown here.

You didn't show anything. I gave the experimental meaning of your framework $ab=c$, in precisely the same way as any physical framework gets its physical meaning:

whenever you have something behaving like a and b, the product behaves like c..

 

[Dale]

I gave the experimental meaning of your framework ab=cab=cab=c, in precisely the same way as any physical framework gets its physical meaning:

Nonsense, you cannot do an experiment with only that “experimental meaning”. It is insufficient for applying the scientific method.

Suppose I do an experiment and measure 6 values: 1, 2, 3, 4, 5, 6. Using only the above framework and your supposed “experimental meaning” do the measurements verify or falsify the theory?